In Peskin and Schroeder's Quantum Field Theory, there is an identity of Pauli matrices which is connected to the Fierz identity, (equation 3.77) (σμ)αβ(σμ)γδ=2ϵαγϵβδ. The author explains that
One can understand the identity by noting that the indices α,γ transform in the Lorentz representation of ΨL, while β,δ transform in the separate representation of ΨR, and the whole quantity must be a Lorentz invariant.
How can one see α,γ and β,δ transform in different representation?
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